In present-day optical system design, it is tacitly assumed that local minima are points in the merit function landscape without relationships between them. We will show however that there is a certain degree of order in the design landscape and that this order is best observed when we change the dimensionality of the optimization problem and when we consider not only local minima, but saddle p...

Bundle Adjustment is a common technique to improve results of any multiple view reconstruction algorithm to obtain 3D structure for computer vision and computer graphics. If the error of a reconstruction can be expressed by an error function, this function can be minimized by numerical methods such as the Levenberg-Marquardt algorithm. By this means, the reconstruction can often be significantl...

In this paper, we present constrained simulated annealing (CSA), a global minimization algorithm that converges to constrained global minima with probability one, for solving nonlinear discrete non-convex constrained minimization problems. The algorithm is based on the necessary and suucient condition for constrained local minima in the theory of discrete Lagrange multipliers we developed earli...

An algorithm for finding an approximate global minimum of a funnel shaped function with many local minima is described. It is applied to compute the minimum energy docking position of a ligand with respect to a protein molecule. The method is based on the iterative use of a convex, general quadratic approximation that underestimates a set of local minima, where the error in the approximation is...

Global energy optimization of a molecular system is difficult due to the well-known “multiple minimum” problem. The rugged potential energy surface (PES) characteristic of multidimensional systems can be transformed reversibly using potential smoothing to generate a new surface that is easier to search for favorable configurations. The diffusion equation method (DEM) is one example of a potenti...

With the formation of the competitive electricity markets in the world, optimization of bidding strategies has become one of the main discussions in studies related to market designing. Market design is challenged by multiple objectives that need to be satisfied. The solution of those multi-objective problems is searched often over the combined strategy space, and thus requires the simultaneous...

Accurate modelling of real-world problems often requires nonconvex terms to be introduced in the model, either in the objective function or in the constraints. Nonconvex programming is one of the hardest fields of optimization, presenting many challenges in both practical and theoretical aspects. The presence of multiple local minima calls for the application of global optimization techniques. ...

Ab initio calculations at the CCSD(T)/aug-cc-pVTZ level of theory were used to characterize the Ar-CH(3)OH intermolecular potential energy surface (PES). Potential energy curves were calculated for four different Ar + CH(3)OH orientations and used to derive an analytic function for the intermolecular PES. A sum of Ar-C, Ar-O, Ar-H(C), and Ar-H(O) two-body potentials gives an excellent fit to th...